This is just the problem: we can't just tune out unwanted sounds with the same ease that NTs seem to be able to. They can ignore sound easily, but we can't. This is an autistic trait, and something that you should explain to your mother.
Also, it's all about controling sensory input: my music doesn't bother me when I'm listening to it, because it's my music and I'm in control of it, but if I go out to a restaurant, then the nosie really would bother me, because I can't tune out background noise when trying to talk to people. Other people don't have this problem and like the music because it creates atmosphere.
My partner has the TV on non-stop when he's in the house, I can hear it all the time and it drives me nuts. It's too loud and stops me from working and concentrating. I also like to listen to music and just as I can hear the TV upstairs, my music can be heard downstairs in the living room where my partner is when he is watching TV, but it neve seems to bother him - he just tunes it out! I wish I could do the same but I can't.